Skip to main content
SpringerLink
Log in

Geometrical CP violation in the N-Higgs-doublet model

  • Regular Article - Theoretical Physics
  • Published:
The European Physical Journal C Aims and scope Submit manuscript

Abstract

Geometrical CP violation is a particular type of spontaneous CP violation in which the vacuum expectation values have phases which are calculable, i.e. stable against the variation of the free parameters of the scalar potential. Although originally suggested within a specific version of the three-Higgs-doublet model, it is a generic phenomenon. We investigate its viability and characteristic features in models with several Higgs doublets. Our work contains both general results and illustrative examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. A different form of spontaneous CP violation, in which it occurs in spite of all the VEVs being real, has been proposed in Ref. [8].

  2. The statement that the relative phases of the VEVs in geometrical CP violation do not depend on the free parameters of the potential is sometimes found. This statement is somewhat misleading since those parameters must be such that the CP-violating VEV alignment is the global minimum of the potential. A better definition of calculable phases is that they are phases which are stable against reasonably large variations of the free parameters of the potential.

  3. See for instance [18].

  4. The relevance of the regular pentagon to geometrical CP violation with N=5 was also noted in Ref. [11, 12].

  5. Equation (60b) may be derived in the following way. Consider four planar vectors \(\vec{n}_{1}\), \(\vec{n}_{2}\), \(\vec{n}_{3}\), and \(\vec{n}_{4}\), all of them with unit length and with polar angles ψ 1, ψ 2, −ψ 3, and −ψ 4, respectively. We define two vectors \(\vec{p} = \vec{n}_{1} + \vec{n}_{3}\) and \(\vec{q} = \vec{n}_{2} + \vec{n}_{4}\). Then,

    On the other hand, J is the projection of \(\vec{p} + \vec{q}\) on the horizontal axis. Then,

References

  1. G.C. Branco, L. Lavoura, J.P. Silva, CP Violation (Oxford University Press, Oxford, 1999)

    Google Scholar 

  2. T.D. Lee, Phys. Rev. D 8, 1226 (1973)

    Article  ADS  Google Scholar 

  3. G.C. Branco, A.J. Buras, J.M. Gerard, Nucl. Phys. B 259, 306 (1985)

    Article  ADS  Google Scholar 

  4. M. Maniatis, A. von Manteuffel, O. Nachtmann, Eur. Phys. J. C 57, 739 (2008)

    Article  ADS  Google Scholar 

  5. M. Maniatis, O. Nachtmann, J. High Energy Phys. 0905, 028 (2009)

    Article  ADS  Google Scholar 

  6. P.M. Ferreira, J.P. Silva, Eur. Phys. J. C 69, 45 (2010)

    Article  ADS  Google Scholar 

  7. G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher, J.P. Silva, Phys. Rep. 516, 1 (2012)

    Article  ADS  Google Scholar 

  8. L. Lavoura, Phys. Lett. B 400, 152 (1997)

    Article  ADS  Google Scholar 

  9. G.C. Branco, J.-M. Gérard, W. Grimus, Phys. Lett. 136B, 383 (1984)

    ADS  Google Scholar 

  10. I. de Medeiros Varzielas, D. Emmanuel-Costa, P. Leser, Phys. Lett. B 716, 193 (2012)

    Article  ADS  Google Scholar 

  11. I. de Medeiros Varzielas, D. Emmanuel-Costa, Phys. Rev. D 84, 117901 (2011)

    Article  ADS  Google Scholar 

  12. I. de Medeiros Varzielas, J. High Energy Phys. 1208, 055 (2012)

    Article  Google Scholar 

  13. A. Degee, I.P. Ivanov, V. Keus, J. High Energy Phys. 1302, 125 (2013)

    Article  ADS  Google Scholar 

  14. M. Holthausen, M. Lindner, M.A. Schmidt. arXiv:1211.6953 [hep-ph]

  15. B. Petersen, M. Ratz, R. Schieren, J. High Energy Phys. 0908, 111 (2009)

    Article  ADS  Google Scholar 

  16. R. Schieren. arXiv:1102.4611 [hep-ph]

  17. I.P. Ivanov, V. Keus, E. Vdovin, J. Phys. A 45, 215201 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  18. V.A. Solano, J.A. Armario-Sampalo, M.D. Frau-García, P. Real-Jurado, Mathematica notebook IntegerSmithNormalForm, Wolfram Library Archive. http://library.wolfram.com/infocenter/MathSource/6621

Download references

Acknowledgements

The work of I.P.I. was supported in part by the grant RFBR 11-02-00242-a, the RF President Grant for scientific schools NSc-3802.2012.2, and the Program of the Department of Physics of the Scientific Council of the Russian Academy of Sciences “Studies of Higgs boson and exotic particles at LHC.” The work of L.L. was supported by Portuguese national funds through the project PEst-OE/FIS/UI0777/2011 of the Fundação para a Ciência e a Tecnologia.

Author information

Authors and Affiliations

  1. IFPA, Université de Liège, Allée du 6 Août 17, bâtiment B5a, 4000, Liège, Belgium

    I. P. Ivanov

  2. Sobolev Institute of Mathematics, Koptyug avenue 4, 630090, Novosibirsk, Russia

    I. P. Ivanov

  3. CFTP, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001, Lisboa, Portugal

    L. Lavoura

Authors
  1. I. P. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Lavoura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. P. Ivanov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivanov, I.P., Lavoura, L. Geometrical CP violation in the N-Higgs-doublet model. Eur. Phys. J. C 73, 2416 (2013). https://doi.org/10.1140/epjc/s10052-013-2416-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjc/s10052-013-2416-8

Keywords

Search

Navigation